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tanh(z) is (e^z-e^-z)/(e^z+e^-z)
and e^(i*pi/2) is i, e^(-i*pi/2) is -i, so 2i/0.
2i/0 is nan + nani I think, though am not 100% sure about that.
The fact that sinh/cosh gives different number is just a matter of imprecise
calculations.

2*i/0 is Inf (or i*Inf, if it matters) (0/2i is obviously 0).
(One way of thinking about these is to write z = r*exp(i*w), where r is real
amplitude and w is real phase. This way say lim(x/y) == lim((r_x)/(r_y)).)
I noticed the bug while calculatin coth(i*x) as 1/tanh(i*x).
coth(i*pi/2) must be zero.
Also the difference between (0 + -4.48966e-11i) and (nan + nani) is
more than machine precision.
The bottom line is: glibc in FC3 got it right and in FC4 does not.

Fair enough. The correct(ed) statement is that the test program gives right
answers in FC3 and wrong answers in FC4 and that needs fixing.
Also, this is might be somewhat off-topic, but there is a FDLIBM math library
on netlib which as far as I can tell has GNU-compatible license (it is developed
at Sun). This library often used as a reference library for math functions.
Any reason GNU libm cannot use it?
Sincerely,
Dmitri.